For a gas of nitrogen molecules (N2), what must the temperature b...

Question

For a gas of nitrogen molecules (N2), what must the temperature be if 94.7% of all the molecules have speeds less than (a) 1500 m/s? Use Table 18.2. The molar mass of N2 is 28.0 g/mol

Accepted Answer

Hey everyone in this problem, we are told that 97.9% of oxygen molecules in a metallic container have speeds below 1200 m/s. Okay, we're asked to determine the temperature of the sample. We're told that V divided by V R. M. S is equal to 1.8 and that the molar mass of oxygen is 32 g per mole. Alright, We're talking about temperature. Okay? We have information about temperature. We have information about speed. So let's recall how we can relate the two. Okay, We know that the R. M. S. Is equal to the square root of three. R. T over big M. Okay. Where T. Is the temperature is similar mass. R. Is the gas constant? And V RMS is the root mean square speed. Alright, So we have our and we know the molar mass. M. Okay? So in order to find temperature, the only thing we need is V R M. S. Well, let's use the hint. We've been given, Okay, we've been given that V divided by VRM. S is equal to 1.8. Okay. Were also given a speed in the problem of 1200 m/s. So we know that 1200 m per second divided by the R M. S. Is equal to 1.8. Well, this means that V R M. S is equal to 1200 divided by 1. m per second. And we get a V R M. S of 666.66 repeated meters per second. Okay, So now we have the R. M. S. We have our we have M. And so we can use the equation on the left side to find the temperature. T. Okay, so substituting the values we know 666.66 repeated meters per second is equal to the square root. Just do a dotted line. So we can keep our work separate of three times are or as a gas constant K. Look this up in your table in your textbook or that your professor provided? 8.314. Okay. And the unit here is jewel per mole kelvin. Hey times temperature divided by m the molar mass. Now the molar mass were given is in grams per mole. We want to convert this to our standard units. We want kilograms per mole. So we're gonna have 0. kilograms per mole. Okay. The unit Permal will cancel from the numerator and the denominator. I'm squaring both sides. On the left hand side. We're gonna get 4.44 repeated Times 10 to the five when we're squaring. So we have meters squared per second squared. And on the right hand side we're gonna have three times 8.314. Okay, so we have 942. The units we have remaining are jewels per Calvin. Okay. And jewel is a kilogram meter squared per second squared. So let's write it in terms of that kilogram meter squared per second squared. We still have the unit of kelvin and the denominator times. T. Alright. Divided by 0.032 kg. Okay. The unit of kilogram will cancel the meter squared per second squared we have on both sides so we can divide and that will also cancel. And we're going to be left with the unit of Calvin. Okay, so multiplying and dividing, we're going to get T. The temperature is equal to 570 point to Calvin. That is the temperature of the oxygen sample. That's going to correspond with answer B. That's it for this one. Thanks everyone for watching. See you in the next video.

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